modeling and simulation of a small wind turbine …

Carpathian Journal of Electrical Engineering Volume 7, Number 1, 2013

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MODELING AND SIMULATION OF A SMALL WIND TURBINE

USING MATLAB SIMULINK

Dumitru POP, Radu TÎRNOVAN, Liviu NEAMŢ, Dorin SABOU

Technical University of Cluj Napoca.

[email protected]

Keywords: Wind energy, Modeling, Simulation, Matlab

Abstract: In this paper, a small wind turbine is analyzed. Because usually the manufactures don’t provide

enough information about the turbine (especially for small turbines), the steps for obtaining this parameters are

presented. A Matlab program was written to fulfill this steps and then the whole turbine was simulated in

Simulink. The resulted performance curve from simulation was compared with the performance curve from the

manufacture’s datasheet for validation

1. INTRODUCTION

In recent years, the demand for renewable energy increased due to environmental

problems, high conventional fuels prices and shortage of traditional energy sources in the near

future. [1] [2] Of all available renewable resources, solar and wind energy are attracting the

most attention due to its abundant, inexhaustible potential and its increasingly competitive

cost. Wind technologies have been developing rapidly over the last few decades being

considered one of the most important sustainable energy resources and one of the best

technologies today to provide a sustainable electrical energy supply to the world

development. [3] [4]

The utilization of wind energy has a very long tradition, being used first to move

ships. Later, the Persians invented the windmill to pump water and grind crops. Nowadays,

wind turbines are used to convert wind energy into electricity. The main problem of wind

energy is that its availability depends on climate conditions and terrain. Also, the "quality" of

the wind is very important because even if the speed it's good, turbulences produced by trees


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or hills (in cities by buildings) will affect the energy production and can damage the turbine.

[5] [6]

In terms of the generators for wind-power application, there are two big concepts:

fixed-speed and variable-speed wind turbine generators. Permanent magnet synchronous

generators (PMSG) are increasingly popular due to their advantages of small size, high energy

density, low maintenance cost, and ease of control. [2] [3] Large wind turbines are complex in

operation, deploy multitude of control methods and operate in grid-connected mode. On the

other hand, small wind turbines can be used for grid-connected system as well as stand-alone

system for remote places where grid based electricity is not available. [7] [8]

In order to simulate a wind turbine, some information about it must be known.

Unfortunately, the manufactures don’t provide enough specifications in their data sheets,

especially for small scale turbines. Usually, they provide only the power curve (with respect

to wind speed) and some information about rotor diameter and weight. This paper will present

a method to obtain the parameters needed for simulations using Matlab Simulink.

2. WIND ENERGY CONVERSION

The kinetic energy of the wind is given by the following equation:

𝐸 =𝑚∙𝑣2

2 [Nm] (1)

where v is the wind speed (m/s) and m is the air mass determined by air density ρ and volume

that crosses a certain surface A in time t:

𝑚 = 𝜌 ∙ 𝐴 ∙ 𝑣 ∙ 𝑡[kg/s] (2)

The wind power Pw has the following expressions:

𝑃𝑤 =𝜌∙𝐴∙𝑣3

2 [W] (3)

The power extracted from the wind by a wind turbine is given by:

𝑃 = 𝐶𝑝 ∙ 𝑃𝑣 = 𝐶𝑝 ∙𝜌∙𝐴∙𝑣3

2 [W] (4)

where Cp is the power coefficient and it’s given as a function of the tip speed ratio λ and the

blade pitch angle. The pitch angle is the angle between the plane of rotation and the blade

cross section chord. [9] The tip speed ratio of a wind turbine is defined as:

𝜆 =𝑢

𝑣=

𝜔𝑅

𝑣 (5)

where: u is the tangential velocity of the blade pitch, ω is the angular velocity of the rotor

(rad/s), R is the rotor radius (m), and v the wind speed (m/s).

In Fig. 1 the approximation of the real rotor power curve by various theoretical

approaches is presented. [1]. Usually three-blade airflow wind turbines are used for electric

energy generation because, they have the highest power coefficient.


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Fig. 1 – Approximation of the real rotor power curve by various theoretical approaches [1]

3. SIMULATION AND RESULTS

In this paper a wind turbine fabricated by Southwest Windpower Inc. is analyzed.

Table1 presents the specifications of the wind turbine, model AirX 400, and in Fig. 2 the

power curve with respect to wind speed.

Table1. Parameters of wind turbine AirX 400

Power 400 W

Voltage 24V

Rotor diameter 1.15 m

Cut in wind speed 2.5 m/s

Cut out speed 13 m/s

Weight 5.85 kg

Blades 3

Fig. 2 – AirX 400 performance curve


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This wind turbine was analyzed using Matlab. It must be specified that the analyze

was made for the interval between no wind speed and cut-out wind speed, i.e. for wind speed

ranging between 0 to 13 m/s. In order to find the parameters needed for simulations these

steps were made:

the values of power in respect with wind speed were extracted from Fig. 2;

the Cp values in respect with λ were extracted from Fig. 1 (for a 3 blade wind turbine);

from eq. (4), Cp was computed for every value of power;

with eq. (3) we computed the power of the wind;

with eq. (4) we computed the power of the wind turbine.

In order to fulfill these steps, a Matlab program was written. A screenshot with a part

of this program is presented in Fig. 3.

Fig. 3 – Screen shoot with a part of the program written in Matlab

After running the Matlab program, the parameters needed for the simulation are

loaded in Matlab’s workspace. In Fig. 4 is presented the differences between the theoretical

Cp(λ) and the obtained curve after simulation. Also, from Fig. 4 we can see that the power

coefficient is ranging from 0 to 0.27 for this wind turbine. In Fig. 5 we can see the output

power of the wind generator in respect with wind speed and angular speed of the rotor.

In Fig. 6 is presented the wind turbine system implemented in Matlab Simulink. This

model has as input parameter the wind speed (the “Ramp” block from Simulink library). The

permanent magnet synchronous machine block has a negative input in order to act as a

generator (positive for motor and negative for generator).


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Fig. 4 – Differences between the theoretical Cp(λ) and the obtained curve after simulation

Fig. 5 – Output power of the wind generator in respect with wind speed and angular speed of the rotor

Fig. 6 – The wind turbine system implemented in Matlab Simulink


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The “Power (wind speed, angular speed)” block (“Lookup2D” in Simulink library)

outputs a power value using interpolation-extrapolation method with respect to the input

values of wind speed and angular speed. The data needed for this block were obtained after

running the Matlab program presented in Fig. 3.

For the validation, the power curve obtained after simulations was compared with the curve

from the manufacturer (Fig. 7). As it can be seen, there is a good match between those two curves.

3. CONCLUSIONS

In this paper, a small wind turbine was analyzed. Because usually manufactures don’t

provide enough information about the wind turbine, a Matlab program was written in order to

find out some parameters needed for simulation. Then, using blocks from Matlab Simulink

library, a wind turbine was implemented. The resulted performance curve from the model was

compared with the curve from the manufacture’s datasheet for validation.

ACKNOWLEDGMENT: This paper was supported by the project "Improvement of the

doctoral studies quality in engineering science for development of the knowledge based

society-QDOC” contract no. POSDRU/107/1.5/S/78534, project co-funded by the European

Social Fund through the Sectorial Operational Program Human Resources 2007-2013.

REFERENCES

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Springer, 2005.

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Synchronous Generator for Integration, Power Engineering Society General Meeting, 2007. IEEE, pp.


37

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